In an asexual population adapting to a new environment, different beneficial mutations compete for fixation. This effect, known as clonal interference, has been invoked as an explanation for the prevalence of sexual reproduction in higher organisms. The talk will review the theory of clonal interference, and show that a simple approximation based on extremal statistics arguments works well in the parameter range of experimental interest. A key assumption is that different beneficial mutations interact multiplicatively. Based on empirical fitness data for the asexual fungus Aspergillus niger I will show that this is generally not true, and that the benefits of sex are quite limited when realistic fitness interactions are taken into account. The talk is based on joint work with Su-Chan Park and Arjan de Visser.